Exploring two-spin internal linear combinations for the recovery of the CMB polarization

TL;DR

This paper introduces a novel linear combination method for CMB polarization recovery that preserves the physical coherence of the polarization angle across frequencies, improving upon previous techniques.

Contribution

It proposes a two-spin internal linear combination approach that accounts for frequency-dependent polarization phase shifts, enhancing CMB polarization analysis.

Findings

Achieved residual levels comparable to existing ILC methods.

Successfully simulated polarization rotation effects like Faraday rotation.

Demonstrated the method's ability to handle frequency-dependent polarization phase shifts.

Abstract

We present a methodology to recover cosmic microwave background (CMB) polarization in which the quantity $P = Q+ iU$ is linearly combined at different frequencies using complex coefficients. This is the most general linear combination of the $Q$ and $U$ Stokes parameters which preserves the physical coherence of the residual contribution on the CMB estimation. The approach is applied to the internal linear combination (ILC) and the internal template fitting (ITF) methodologies. The variance of $P$ of the resulting map is minimized to compute the coefficients of the linear combination. One of the key aspects of this procedure is that it serves to account for a global frequency-dependent shift of the polarization phase. Although in the standard case, in which no global E-B transference depending on frequency is expected in the foreground components, minimizing $\left\langle |P|^2\right\rangle$ is similar to minimizing $\left\langle Q^2\right\rangle$ and $\left\langle U^2\right\rangle$ separately (as previous methodologies proceed), multiplying $Q$ and $U$ by different coefficients induces arbitrary changes in the polarization angle and it does not preserve the coherence between the spinorial components. The approach is tested on simulations, obtaining a similar residual level with respect to the one obtained with other implementations of the ILC, and perceiving the polarization rotation of a toy model with the frequency dependence of the Faraday rotation.